Electron. J. Differential Equations, Vol. 2017 (2017), No. 63, pp. 1-18.

Holder continuity of bounded generalized solutions for nonlinear fourth-order elliptic equations with strengthened coercivity and natural growth terms

Mykhailo V. Voitovych

In this article we extend the author's previous results on the existence of bounded generalized solutions of a Dirichlet problem for nonlinear elliptic fourth-order equations with the principal part satisfying a strengthened coercivity condition, and a lower-order term having a "natural" growth with respect to the derivatives of the unknown function. Namely, we prove the Holder continuity of bounded generalized solutions of such equations.

Submitted November 11, 2016. Published March 2, 2017.
Math Subject Classifications: 35B45, 35B65, 35J40, 35J62.
Key Words: Nonlinear elliptic equations; strengthened coercivity; lower-order term; natural growth; bounded solution, Holder continuity.

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Mykhailo V. Voitovych
Institute of Applied Mathematics and Mechanics
National Academy of Sciences of Ukraine
Gen. Batiouk Str. 19, 84116 Sloviansk, Ukraine
email: voitovichmv76@gmail.com

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